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Last Lecture Everything you need to know about dynamics of rotation Today PowerPoint PPT Presentation


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Last Lecture Everything you need to know about dynamics of rotation Today Pendulums and Kinetic Energy of rotation Important Concepts Equations for angular motion are mostly identical to those for linear motion with the names of the variables changed.

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Last Lecture Everything you need to know about dynamics of rotation Today

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Last lecture everything you need to know about dynamics of rotation today

  • Last Lecture

    • Everything you need to know about dynamics of rotation

  • Today

    • Pendulums and Kinetic Energy of rotation

  • Important Concepts

    • Equations for angular motion are mostly identical to those for linear motion with the names of the variables changed.

    • Kinetic energy of rotation adds a new term to the same energy equation, it does not add a new equation.

    • Kinetic energy can be simply written as a linear term and a rotational term

8.01L IAP 2007


Important reminders

Important Reminders

  • Note that tutors have both assigned and open sessions this week. See web for schedule

  • Mastering Physics due tomorrow at 10pm.

  • Experiment in class on Thursday.

    • Note that if you do NOT do the necessary calculations in advance, there is a good chance that you will NOT be able to finish the experiment in time.

  • Problems-solving in recitation this Friday.

  • Pset due this Friday at 4:30pm.

8.01L IAP 2007


Right hand rule review by request

Right-Hand-Rule Review (by request)

  • Except for the gyroscope, all 8.01L problems can be solved without using R-H-R, use CW/CCW instead.

    • However, many problems in 8.02 require R-H-R

  • The vector for any angular quantity (, , , , J) points along the axis with the direction given by:

    • Fingers curl in direction of , , , , J, thumb points in the direction of the vector

  • Cross-product Right-Hand-Rule: Fingers point along vector A, curl fingers to point along vector B, thumb points in direction C.

8.01L IAP 2007


Pendulums

Pendulums

  • Simple pendulum: Small mass at the end of a string

    • Period is where l is the length from the pivot to the center of the object.

  • Physical pendulum: More complex object rotating about any pivot

    • Period is where l is the distance from the pivot to the center of mass of the object, M is the total mass, and I is the moment of inertia around the pivot.

8.01L IAP 2007


Parallel axis theorum

d

c.m.

Axis 1

Parallel Axis Theorum

  • Very simple way to find moment of inertia for a large number of strange axis locations.

  • I1 = Ic.m. + Md2 where M is the total mass.

8.01L IAP 2007


Kinetic energy with rotation

Kinetic Energy with Rotation

  • Adds a new term not a new equation!

  • Rotation around any fixed pivot:

  • Moving and rotating:

8.01L IAP 2007


Everything you need to know for linear rotational dynamics

Everything you need to know for Linear & Rotational Dynamics

  • This is true for anyfixed axis and for an axis through the center of mass, even if the object moves or accelerates.

  • Rolling without slipping:

    • Friction does NOT do work!

  • Rolling with slipping:

    • Friction does work, usually negative.

    • Rarely solvable without using force and torque equations!

  • 8.01L IAP 2007


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